Efficient bayesian learning in non‐linear dynamic models

Pole, Andy; West, Mike

doi:10.1002/for.3980090205

Cited by 21 publications

(6 citation statements)

References 19 publications

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“…12]), developments based on numerical quadrature * [31,45,45], and traditional Monte Carlo * simulation approaches [65].…”

Section: Computation and Simulationmentioning

confidence: 99%

Bayesian Forecasting

West¹

2005

Encyclopedia of Statistical Sciences

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Bayesian forecasting encompasses statistical theory and methods in time series * analysis and time series forecasting * , particularly approaches using dynamic and state-space models, though the underlying concepts and theoretical foundation relate to probability modeling and inference more generally. This entry focuses specifically on time series and dynamic modeling, with mention of related areas.

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“…12]), developments based on numerical quadrature * [31,45,45], and traditional Monte Carlo * simulation approaches [65].…”

Section: Computation and Simulationmentioning

confidence: 99%

Bayesian Forecasting

West¹

2005

Encyclopedia of Statistical Sciences

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“…Kramer and Sorenson (1988) adhered to the same methodology, but opted for a constant interpolating function. Pole and West (1990) have attempted to reduce the problem of choosing the grid's location by implementing a dynamic grid allocation method.…”

Section: Direct Numerical Integrationmentioning

confidence: 99%

Sequential Monte Carlo Methods to Train Neural Network Models

et al. 2000

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We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/ sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices.

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“…The non-linearity of h(x(t)) in the observation equation means that the observations will in general be non-Gaussian and so conventional Kalman filtering is inappropriate. One could proceed with the model directly (see Jazwinski, 1970) and determine the various conditional distributions involved through a mix of simulation (see Kitagawa, 1987;Pole and West, 1990) and exact results (see Harvey and Shephard, 1993, for example). A detailed discussion of techniques for non-linear dynamic model fitting and prediction is given in Ozaki et al (1997).…”

Section: Computational Proceduresmentioning

confidence: 99%

A non‐linear dynamic model for multiplicative seasonal‐trend decomposition

Ozaki

Thomson

2002

Journal of Forecasting

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A non-linear dynamic model is introduced for multiplicative seasonal time series that follows and extends the X-11 paradigm where the observed time series is a product of trend, seasonal and irregular factors. A selection of standard seasonal and trend component models used in additive dynamic time series models are adapted for the multiplicative framework and a non-linear filtering procedure is proposed. The results are illustrated and compared to X-11 and log-additive models using real data. In particular it is shown that the new procedures do not suffer from the trend bias present in log-additive models.

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Efficient bayesian learning in non‐linear dynamic models

Abstract: This paper demonstrates the practical application of recently developed techniques of efficient numerical analysis for dynamic models. The models presented share a common basic structural foundation but nevertheless cover a very large arena of possible applications, as will be shown.

Cited by 21 publications

References 19 publications

Bayesian Forecasting

Bayesian Forecasting

Sequential Monte Carlo Methods to Train Neural Network Models

A non‐linear dynamic model for multiplicative seasonal‐trend decomposition

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